Sequence Generators in Digital Circuits
Sequence
Generators
:
I=
(Q
1
, Q
2
,
Q
i
)
The
PN
sequence length is the number
of
iterations (the number
of
1s and
0s)
before the sequence
repeats.
The sequence length is determined
by
the:
–
number
of
flip flops,
n
,
in the shift
register
–
Selection
of
feedback
taps
that
are
applied
to
one
or
more XOR
gates.
The sequence length
can
have
a
maximum
value
of:
Maximum
PN
sequence length
=
𝟐
𝒏
-
1
where
n
is the number
of flip-
flops.
28
Maximal
length
sequence=
S
S≤
𝟐
𝒏
-1
Example
1
:
Design
a
sequence generator
to
generate the sequence pattern
100010011010111
Solution:
S≤
𝟐
𝒏
-
1
for S=
1
5
n=4
I
=
𝐂D
+
C
𝐃
=
C
D
29
Note:
When the feedback logic include
any
XOR gates the resulting circuit it called
(Linear PN) otherwise it's called (non Linear
PN).
H.W:
Design
a
sequence generator to generate
the
sequence pattern:
111101011001000
Example
2:
Design
a sequence
generator to the prescribed sequence
1011110.
Solution:
S≤
𝟐
𝒏
- 1
S =7
n=3
30
Note:
If
there is similar states we need to add another stage to
remove
similarity.
A
B
0
0
01
11
10
31
CD
00
01
11
10
𝐈 =
𝐀
̅
+
𝐂
̅
+
𝐃
̅
I
=A.C.D
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Note:
The
Karnaugh
map for five variables will
be
as
shown in the
figure
below:
Explore the concept of sequence generators in digital circuits, focusing on PN sequence lengths, feedback taps, XOR gates, and designing patterns with examples and visual aids, including Karnaugh maps.
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Presentation Transcript
Sequence Generators: I= (Q1, Q2, Qi) The PN sequence length is the number of iterations (the number of 1s and 0s) before the sequence repeats. The sequence length is determined by the: number of flip flops, n, in the shift register Selection of feedback taps that are applied to one or more XOR gates. The sequence length can have a maximum value of: Maximum PN sequence length = ??- 1 where n is the number of flip- flops. 28 Maximal length sequence= S S ??-1 Example 1: Design a sequence generator to generate the sequence pattern 100010011010111 Solution: S ??-1 for S=15 n=4 D 1 1 1 1 0 0 0 1 A 1 0 0 0 1 0 0 1 C 1 1 1 0 0 0 1 0 B 1 1 0 0 0 1 0 0 I 0 0 0 1 0 0 1 1
0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 I = ?D + C? = C D 29
Note: When the feedback logic include any XOR gates the resulting circuit it called (Linear PN) otherwise it's called (non Linear PN). H.W: Design a sequence generator to generate the sequence pattern: 111101011001000 Example 2: Design a sequence generator to the prescribed sequence 1011110. Solution: S ??- 1 S =7 n=3 30 D 1 1 C 1 0 B 0 1 A 1 0 I 0 1
0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 Note: If there is similar states we need to add another stage to remove similarity. AB 00 01 11 10 CD X X 1 1 X X 1 0 1 X X 0 1 00 X X X 01 11 10 ? = ? + ? + ? I =A.C.D 31
Note: The Karnaugh map for five variables will be as shown in the figure below:
